The noise in the circular law and the Gaussian free field

Fill an n x n matrix with independent complex Gaussians of variance 1/n. As n approaches infinity, the eigenvalues {z_k} converge to a sum of an H^1-noise on the unit disk and an independent H^{1/2}-noise on the unit circle. More precisely, for C^1 functions of suitable growth, the distribution of sum_{k=1}^n (f(z_k)-E f(z_k)) converges to that of a mean-zero Gaussian with variance given by the sum of the squares of the disk H^1 and the circle H^{1/2} norms of f. Moreover, with p_n the characteristic polynomial, log|p_n|- E log|p_n| tends to the planar Gaussian free field conditioned to be harmonic outside the unit disk. Finally, for polynomial test functions f, we prove that the limiting covariance structure is universal for a class of models including Haar distributed unitary matrices.Comment: 30 pages, 5 figures. Revised introduction. New section

Splitting Algorithms for Fast Relay Selection: Generalizations, Analysis, and a Unified View

Relay selection for cooperative communications promises significant performance improvements, and is, therefore, attracting considerable attention. While several criteria have been proposed for selecting one or more relays, distributed mechanisms that perform the selection have received relatively less attention. In this paper, we develop a novel, yet simple, asymptotic analysis of a splitting-based multiple access selection algorithm to find the single best relay. The analysis leads to simpler and alternate expressions for the average number of slots required to find the best user. By introducing a new `contention load' parameter, the analysis shows that the parameter settings used in the existing literature can be improved upon. New and simple bounds are also derived. Furthermore, we propose a new algorithm that addresses the general problem of selecting the best $Q \ge 1$ relays, and analyze and optimize it. Even for a large number of relays, the algorithm selects the best two relays within 4.406 slots and the best three within 6.491 slots, on average. We also propose a new and simple scheme for the practically relevant case of discrete metrics. Altogether, our results develop a unifying perspective about the general problem of distributed selection in cooperative systems and several other multi-node systems.Comment: 20 pages, 7 figures, 1 table, Accepted for publication in IEEE Transactions on Wireless Communication

Optimal Timer Based Selection Schemes

Timer-based mechanisms are often used to help a given (sink) node select the best helper node among many available nodes. Specifically, a node transmits a packet when its timer expires, and the timer value is a monotone non-increasing function of its local suitability metric. The best node is selected successfully if no other node's timer expires within a 'vulnerability' window after its timer expiry, and so long as the sink can hear the available nodes. In this paper, we show that the optimal metric-to-timer mapping that (i) maximizes the probability of success or (ii) minimizes the average selection time subject to a minimum constraint on the probability of success, maps the metric into a set of discrete timer values. We specify, in closed-form, the optimal scheme as a function of the maximum selection duration, the vulnerability window, and the number of nodes. An asymptotic characterization of the optimal scheme turns out to be elegant and insightful. For any probability distribution function of the metric, the optimal scheme is scalable, distributed, and performs much better than the popular inverse metric timer mapping. It even compares favorably with splitting-based selection, when the latter's feedback overhead is accounted for.Comment: 21 pages, 6 figures, 1 table, submitted to IEEE Transactions on Communications, uses stackrel.st

Large deviations of the maximal eigenvalue of random matrices

We present detailed computations of the 'at least finite' terms (three dominant orders) of the free energy in a one-cut matrix model with a hard edge a, in beta-ensembles, with any polynomial potential. beta is a positive number, so not restricted to the standard values beta = 1 (hermitian matrices), beta = 1/2 (symmetric matrices), beta = 2 (quaternionic self-dual matrices). This model allows to study the statistic of the maximum eigenvalue of random matrices. We compute the large deviation function to the left of the expected maximum. We specialize our results to the gaussian beta-ensembles and check them numerically. Our method is based on general results and procedures already developed in the literature to solve the Pastur equations (also called "loop equations"). It allows to compute the left tail of the analog of Tracy-Widom laws for any beta, including the constant term.Comment: 62 pages, 4 figures, pdflatex ; v2 bibliography corrected ; v3 typos corrected and preprint added ; v4 few more numbers adde

Modulation of the UV-B-induced Oxidative Stress and Apoptosis in HaCaT Cell Line with Calluna vulgaris Extract

The reactive oxygen species (ROS) production due to ultraviolet B (UV-B) exposure is extremely harmful to the skin. It causes lesions of DNA, proteins and lipids and leads to cellular death. In the present study the UV-B-induced ROS and subsequent apoptosis in the human keratinocyte cell line (HaCaT) were counterbalanced by a plant extract with antioxidant capacity. Some molecules modulated by common heather (Calluna vulgaris) (CV) extract through which this may exert its photoprotective effects were also identified. The ROS were evaluated with CM-H2DCFDA assay, while apoptosis and Bax-α/Bcl-xL molecules with ELISA. The extract was standardized according to its polyphenolic content and the most important biologically active compounds, such as hyperozid, quercetin, isoquercetin, kampferol were evidenced by high-performance liquid chromatography. The UV-B induced ROS production occurred at its highest level at 2 h after the exposure of the HaCaT cells, while apoptosis later, at 4 h. The most significant changes in Bax-α and Bcl-XL proteins induced by UV-B, as well as the highest effect of the extract on apoptosis, were both registered at 4 h. The CV extract decreased concentration- and time-dependently the UV-B-induced ROS production and prevented apoptosis. These effects of CV occurred, at least to a certain extent, due to the modulation of Bax-α/Bcl-XL proteins. These findings suggest that skin cells could be protected from some of the UV-B-induced harmful effects by the administration of the CV extract, which may be further exploited as a potential photoprotective agent

EphA2-receptor deficiency exacerbates myocardial infarction and reduces survival in hyperglycemic mice

Background We have previously shown that EphrinA1/EphA expression profile changes in response to myocardial infarction (MI), exogenous EphrinA1-Fc administration following MI positively influences wound healing, and that deletion of the EphA2 Receptor (EphA2-R) exacerbates injury and remodeling. To determine whether or not ephrinA1-Fc would be of therapeutic value in the hyperglycemic infarcted heart, it is critical to evaluate how ephrinA1/EphA signaling changes in the hyperglycemic myocardium in response to MI. Methods Streptozotocin (STZ)-induced hyperglycemia in wild type (WT) and EphA2-receptor mutant (EphA2-R-M) mice was initiated by an intraperitoneal injection of STZ (150 mg/kg) 10 days before surgery. MI was induced by permanent ligation of the left anterior descending coronary artery and analyses were performed at 4 days post-MI. ANOVAs with Student-Newman Keuls multiple comparison post-hoc analysis illustrated which groups were significantly different, with significance of at least p < 0.05. Results Both WT and EphA2-R-M mice responded adversely to STZ, but only hyperglycemic EphA2-R-M mice had lower ejection fraction (EF) and fractional shortening (FS). At 4 days post-MI, we observed greater post-MI mortality in EphA2-R-M mice compared with WT and this was greater still in the EphA2-R-M hyperglycemic mice. Although infarct size was greater in hyperglycemic WT mice vs normoglycemic mice, there was no difference between hyperglycemic EphA2-R-M mice and normoglycemic EphA2-R-M mice. The hypertrophic response that normally occurs in viable myocardium remote to the infarct was noticeably absent in epicardial cardiomyocytes and cardiac dysfunction worsened in hyperglycemic EphA2-R-M hearts post-MI. The characteristic interstitial fibrotic response in the compensating myocardium remote to the infarct also did not occur in hyperglycemic EphA2-R-M mouse hearts to the same extent as that observed in the hyperglycemic WT mouse hearts. Differences in neutrophil and pan-leukocyte infiltration and serum cytokines implicate EphA2-R in modulation of injury and the differences in ephrinA1 and EphA6-R expression in governing this are discussed. Conclusions We conclude that EphA2-mutant mice are more prone to hyperglycemia-induced increased injury, decreased survival, and worsened LV remodeling due to impaired wound healing

The Dopamine D3 Receptor Knockout Mouse Mimics Aging-Related Changes in Autonomic Function and Cardiac Fibrosis

Blood pressure increases with age, and dysfunction of the dopamine D3 receptor has been implicated in the pathogenesis of hypertension. To evaluate the role of the D3 receptor in aging-related hypertension, we assessed cardiac structure and function in differently aged (2 mo, 1 yr, 2 yr) wild type (WT) and young (2 mo) D3 receptor knockout mice (D3KO). In WT, systolic and diastolic blood pressures and rate-pressure product (RPP) significantly increased with age, while heart rate significantly decreased. Blood pressure values, heart rate and RPP of young D3KO were significantly elevated over age-matched WT, but similar to those of the 2 yr old WT. Echocardiography revealed that the functional measurements of ejection fraction and fractional shortening decreased significantly with age in WT and that they were significantly smaller in D3KO compared to young WT. Despite this functional change however, cardiac morphology remained similar between the age-matched WT and D3KO. Additional morphometric analyses confirmed an aging-related increase in left ventricle (LV) and myocyte cross-sectional areas in WT, but found no difference between age-matched young WT and D3KO. In contrast, interstitial fibrosis, which increased with age in WT, was significantly elevated in the D3KO over age-matched WT, and similar to 2 yr old WT. Western analyses of myocardial homogenates revealed significantly increased levels of pro- and mature collagen type I in young D3KO. Column zymography revealed that activities of myocardial MMP-2 and MMP-9 increased with age in WTs, but in D3KO, only MMP-9 activity was significantly increased over age-matched WTs. Our data provide evidence that the dopamine D3 receptor has a critical role in the emergence of aging-related cardiac fibrosis, remodeling, and dysfunction

Conformational Determinants of Phosphotyrosine Peptides Complexed with the Src SH2 Domain

The inhibition of specific SH2 domain mediated protein-protein interactions as an effective chemotherapeutic approach in the treatment of diseases remains a challenge. That different conformations of peptide-ligands are preferred by different SH2 domains is an underappreciated observation from the structural analysis of phosphotyrosine peptide binding to SH2 domains that may aid in future drug design. To explore the nature of ligand binding, we use simulated annealing (SA) to sample the conformational space of phosphotyrosine-containing peptides complexed with the Src SH2 domain. While in good agreement with the crystallographic and NMR studies of high-affinity phosphopeptide-SH2 domain complexes, the results suggest that the structural basis for phopsphopeptide- Src SH2 interactions is more complex than the “two-pronged plug two-hole socket” model. A systematic study of peptides of type pYEEX, where pY is phosphotyrosine and X is a hydrophobic residue, indicates that these peptides can assume two conformations, one extended and one helical, representing the balance between the interaction of residue X with the hydrophobic hole on the surface of the Src SH2 domain, and its contribution to the inherent tendency of the two glutamic acids to form an α-helix. In contrast, a β-turn conformation, almost identical to that observed in the crystal structure of pYVNV bound to the Grb2 SH2 domain, predominates for pYXNX peptides, even in the presence of isoleucine at the third position. While peptide binding affinities, as measured by fluorescence polarization, correlate with the relative proportion of extended peptide conformation, these results suggest a model where all three residues C-terminal to the phosphotyrosine determine the conformation of the bound phosphopeptide. The information obtained in this work can be used in the design of specific SH2 domain inhibitors